In this paper we consider time-decomposition methods and present interesting model problems as benchmark problems in order to study the numerical analysis of the proposed methods. For the time-decomposition methods we discuss the iterative operator-splitting methods with re- spect to the stability and consistency. The main idea for deriving the error estimates is the Taylor expansion in time of the linearized opera- tors. The stability analysis is based on the A-stability of ordinary differ- ential equations, and the importance of including weighted parameters for relaxing the iterative operator-splitting methods can be seen. The exactness and the effciency of the methods are investigated through so- lutions of nonlinear model problems of parabolic differential equations, for example systems of convection-reaction-discussion equations. Finally we discuss the future works and the usefulness of this study in real-life applications. Mathematics Subject

IMF is publishing refereed, high quality original research papers in all areas of pure and applied mathematics as well as refereed, high quality survey papers, expository papers; research announcements describing new results; short notes on unsolved problems, etc.